Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}x+9y &= 8 \\ 4x+6y &= 2\end{align*}$
Begin by moving the $x$ -term in the second equation to the right side of the equation. $6y = -4x+2$ Divide both sides by $6$ to isolate $y$ $y = {-\dfrac{2}{3}x + \dfrac{1}{3}}$ Substitute this expression for $y$ in the first equation. $x+9({-\dfrac{2}{3}x + \dfrac{1}{3}}) = 8$ $x - 6x + 3 = 8$ Simplify by combining terms, then solve for $x$ $-5x + 3 = 8$ $-5x = 5$ $x = -1$ Substitute $-1$ for $x$ back into the top equation. $ -1+9y = 8$ $-1+9y = 8$ $9y = 9$ The solution is $\enspace x = -1, \enspace y = 1$.